MATH251_FA2010_final_exam_guide - 7 Steady-state solution...

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MATH 251 FALL SEMESTER 2010 Final Exam study guide Exam Date/Time : Wednesday, December 15, 2010, from 4:40 to 6:30 pm Format : 150 points in 18 questions. The exam is cumulative, with approx. 60% based on new (chapter 10) material. Location : 010 Sparks (sections 1, 7, 9), 121 Sparks (sections 6, 8, 11, 12), 112 Buckhout (sections 2, 10), 112 Kern (sections 3, 4, 5) A table of Laplace transforms (a copy of table 6.2.1 from the textbook) will be provided during the exam. Topics to study All the topics from the midterm exams: Plus, 1. Separation of variables 2. Two-point eigenvalue problems; finding eigenvalues / eigenfunctions 3. Fourier series; Euler-Fourier formulas 4. The Fourier Convergence Theorem 5. Even and odd functions; even and odd periodic extensions 6. Solution of heat conduction problems (w/ different boundary conditions)
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Unformatted text preview: 7. Steady-state solution of the heat conduction equation 8. Wave equation: vibration of a fixed-end elastic string The topics below are explicitly NOT covered on the final exam: a. Mixing/compound interest/air resistance problems b. Reduction of order c. Predator-prey equations d. D’Alembert solution of the wave equation d. Lapalce/potential equation (section 10.8; note that this topic is different from Laplace transforms, which will be on the exam) Comments : Students should know basic integration techniques; partial differentiation; the Existence and Uniqueness theorems; the general long-term behavior of different types of solutions; the behavior of the solutions of various types of mass-spring systems; stability/ phase portrait classifications; Laplace transforms; computing Fourier coefficients and determine the convergence of Fourier series; and each of the steps used to solve a second order linear PDE initial-boundary value problem....
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